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Quantum anomalous Hall state is expected to emerge in Dirac electron systems such as graphene under both sufficiently strong exchange and spin-orbit interactions. In pristine graphene, neither interaction exists; however, both interactions…
In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed…
We study the correlated insulating phases of twisted bilayer graphene (TBG) in the absence of lattice strain at integer filling $\nu=\pm3$. Using the self-consistent Hartree-Fock method on a particle-hole symmetric model and allowing…
The Integer Quantum Hall Effect (IQHE) is a distinctive phase of two-dimensional electronic systems subjected to a perpendicular magnetic field. Thus far, the IQHE has been observed in semiconductor heterostructures and in mono- and…
Charge-neutral graphene in the quantum Hall regime is an example of a quantum Hall ferromagnet in a complex spin-valley space. This system exhibits a plethora of phases, with the particular spin-valley order parameters chosen by the system…
We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics…
Quantum Hall (QH) interferometry provides an archetypal platform for the experimental realization of braiding statistics of fractional QH states. However, the complexity of observing fractional statistics requires phase coherence over the…
Using mean-field theory, we determine the electronic phase diagram of undoped AB-stacked bilayer graphene in the presence of a transverse electric field. In addition to multiple competing electronic instabilities characterized by excitonic…
Among many remarkable qualities of graphene, its electronic properties attract particular interest due to a massless chiral character of charge carriers, which leads to such unusual phenomena as metallic conductivity in the limit of no…
We describe the gated bilayer graphene system when it is subjected to intense terahertz frequency electromagnetic radiation. We examine the electron band structure and density of states via exact diagonalization methods within Floquet…
Fermi surface topology plays an important role in determining the electronic properties of metals. In bulk metals, the Fermi energy is not easily tunable at the energy scale needed for reaching conditions for the Lifshitz transition - a…
We investigate interaction-induced valley domain walls in bilayer graphene in the $\nu=0$ quantum Hall state, subject to a perpendicular electric field that is antisymmetric across a line in the sample. Such a state can be realized in a…
Proximity effects resulting from depositing a graphene layer on a TMD substrate layer change the dynamics of the electronic states in graphene, inducing spin orbit coupling (SOC) and staggered potential effects. An effective Hamiltonian…
Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to…
The parton theory constructs candidate fractional quantum Hall states by decomposing the physical particles into unphysical partons, placing the partons in integer quantum Hall states, and then gluing the partons back into the physical…
Unlike regular electron spin, the pseudospin degeneracy of Fermi points in graphene does not couple directly to magnetic field. Therefore, graphene provides a natural vehicle to observe the integral and fractional quantum Hall physics in an…
Composite fermion metal states emerge in quantum Hall bilayers at total Landau level filling factor $\nu_T$=1 when the tunneling gap collapses by application of in-plane components of the external magnetic field. Evidence of this…
Trilayer graphene in the fractional Quantum Hall Effect regime displays a set of unique interaction-induced transitions that can be tuned entirely by the applied bias voltage. These transitions occur near the anti-crossing points of two…
Interactions among electrons can give rise to striking collective phenomena when the kinetic energy of charge carriers is suppressed. One example is the fractional quantum Hall effect, in which correlations between electrons moving in two…
Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the $\nu=0$ quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero energy gap, the…